The GameStop stuff illustrates exactly what I'm talking about here though, all those people on Robinhood getting force-sold because their ownership of stocks was virtual and the ones actually on the hook to finalize things were the exchange's creditors.

Naturally for a big player putting billions on something they are going to be doing it directly and thus have full legal liability and unlimited potential losses like you say, but I expect losses are probably limited to the collateral amount for regular people in most circumstances, because otherwise it would be a ridiculous mess for the party providing the loans to them.